I don't mean recitation of vedas, mantras, japas or even stotrams, or even any rituals. I mean simple prayers in your own words in any language such as english, such as "Please help me with xyz." or "Please protect me from danger.". Do any of the scriptures talk about such simple prayers? Do they talk about whether Lord Vishnu hears such prayers, listens to them and answers them? Do they say anything about how such prayers should be done? Please quote from the scriptures and provide their translation in english.
Yes , there is a prayer of Lord Vishnu /Krishna in Srimad Bhagavata Purana-Skanda 11- Chapter -27 -Verse 46. This chapter is about Kriya-Yoga i.e. related to worship of Vishnu/Krishna and mentions the procedure of deity worship. This is general prayer for protection /rescue from any problematic situation as well as saving ourselves from this ocean of samsara i.e. misiries ,pain , cycle of birth and death.
शिरो मत्पादयो: कृत्वा बाहुभ्यां च परस्परम् ||
प्रपन्नं पाहि मामीश भीतं मृत्युग्रहार्णवात ||46||
śiro mat-pādayoḥ kṛtvā bāhubhyāḿ ca parasparam
prapannaḿ pāhi mām īśa bhītaḿ mṛtyu-grahārṇavāt
Placing his head at the feet of the Deity, he should then stand with folded hands before the Lord and pray, “O my Lord, please protect me, who am surrendered unto You. I am most fearful of this ocean of material existence, standing as I am in the mouth of death.”
The chapter is also discussing how such prayers should be done. We can read the full procedure of worship and prayer in the chapter. I am just mentioning some of the verses.
द्रव्यैः प्रसिद्धैर्मद्यागः प्रतिमादिष्वमायिनः |
भक्तस्य च यथालब्धैर्हृदि भावेन चैव हि ॥15॥
dravyaiḥ prasiddhair mad-yāgaḥ pratimādiṣv amāyinaḥ bhaktasya ca yathā-labdhair hṛdi bhāvena caiva hi
One should worship Me in My Deity forms by offering the most excellent paraphernalia. But a devotee completely freed from material desire may worship Me with whatever he is able to obtain, and may even worship Me within his heart with mental paraphernalia.
स्तवैरुच्चावचैः स्तोत्रैः पौराणैः प्राकृतैरपि |
स्तुत्वा प्रसीद भगवन्निति वन्देत दण्डवत् ॥ 45 ॥
stavair uccāvacaiḥ stotraiḥ paurāṇaiḥ prākṛtair api stutvā prasīda bhagavann iti vandeta daṇḍa-vat
The devotee should offer homage to the Lord with all kinds of hymns and prayers, both from the Purāṇas and from other ancient scriptures, and also from ordinary traditions. Praying, “O Lord, please be merciful to me!” he should fall down flat like a rod to offer his obeisances.
Do they talk about whether Lord Vishnu hears such prayers, listens to them and answers them?
Yes , Mahabharata - Sabha Parva - Dyuta Parva says so. During her disrobement Draupadi called Vishnu /Krishna/Hari for her protection and Lord Vishnu in the form of Krishna /Hari immediately came to her rescue.
कृष्णं च विष्णुं च हरिं नरं च |
त्राणाय विक्रोशति याज्ञसेनी ||
समावृणोद् वै विविधै सुवस्त्रे: ||46||
P. 132 Vaisampayana continued,--"When the attire of Draupadi was being thus dragged, the thought of Hari, (And she herself cried aloud, saying), 'O Govinda, O thou who dwellest in Dwaraka, O Krishna, O thou who art fond of cow-herdesses (of Vrindavana). O Kesava, seest thou not that the Kauravas are humiliating me. O Lord, O husband of Lakshmi, O Lord of Vraja (Vrindavana), O destroyer of all afflictions, O Janarddana, rescue me who am sinking in the Kaurava Ocean. O Krishna, O Krishna, O thou great yogin, thou soul of the universe, Thou creator of all things, O Govinda, save me who am distressed,--who am losing my senses in the midst of the Kurus.' Thus did that afflicted lady resplendent still in her beauty, O king covering her face cried aloud, thinking of Krishna, of Hari, of the lord of the three worlds. Hearing the words of Draupadi, Krishna was deeply moved. And leaving his seat, the benevolent one from compassion, arrived there on foot. And while Yajnaseni was crying aloud to Krishna, also called Vishnu and Hari and Nara for protection, the illustrious Dharma, remaining unseen, covered her with excellent clothes of many hues
So from this incidence its quite proved that Shree Hari /Vishnu listens to the prayers of devotees and reponds and rescues them , no matter even its a animal. Even there is a prayer by Gajendra (elephant) to lord Vishnu present in Srimad Bhagavata purana when he was in captured by crocodile.